On equivariant and invariant topological complexity of smooth ℤ/_{𝕡}-spheres

Błaszczyk, Zbigniew; Kaluba, Marek

doi:10.1090/proc/13528

On equivariant and invariant topological complexity of smooth $\mathbb {Z}/\!_p$-spheres
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by Zbigniew Błaszczyk and Marek Kaluba PDF

Proc. Amer. Math. Soc. 145 (2017), 4075-4086 Request permission

Abstract:

We investigate equivariant and invariant topological complexity of spheres endowed with smooth non-free actions of cyclic groups of prime order. We prove that semilinear $\mathbb {Z}/_{\!p}$-spheres have both invariants either $2$ or $3$ and calculate exact values in all but two cases. On the other hand, we exhibit examples which show that these invariants can be arbitrarily large in the class of smooth $\mathbb {Z}/_{\!p}$-spheres.

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